Subgroups — C₃×D₅×#460 #14426005

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×SD₁₆	C₂	1	2	yes	maximal, complemented
2	C₃×D₅×#127	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65452	C₂	1	2	yes	maximal, complemented
6	C₃×#65364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65316	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65137	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₅×#102	C₂	1	2	yes	maximal, complemented
11	C₃×#65051	C₂	1	2	yes	maximal, complemented
12	D₅×#460	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄×D₅	—	2	1	no	—
15	C₂×C₃×D₄×D₅	—	2	1	no	—
16	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
18	C₃×C₅×#127	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×#688	C₂²	1	2	yes	complemented
22	C₃×#4086	—	2	1	no	—
23	C₃×#4086	—	2	1	no	—
24	C₃×#4086	C₂²	1	2	yes	—
25	C₂×C₃×#687	C₂²	1	2	yes	complemented
26	C₃×D₅×SD₁₆	—	2	8	no	—
27	C₂×C₃×#677	C₂²	1	2	yes	complemented
28	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
29	C₃×D₅×C₄⋊C₄	—	2	1	no	—
30	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×#4033	—	2	1	no	—
32	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
33	C₃×#4020	C₂²	1	1	yes	characteristic
34	C₃×C₄²×D₅	—	2	1	no	—
35	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
36	C₃×C₄×Dic₁₀	—	2	1	no	—
37	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₅×#102	C₂²	1	2	yes	complemented
40	C₃×#3964	C₂²	1	2	yes	complemented
41	C₃×#3953	C₂²	1	2	yes	complemented
42	C₃×#3946	C₂²	1	2	yes	complemented
43	C₃×#3941	C₂²	1	2	yes	complemented
44	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#460	—	5	1	no	maximal, Hall
46	C₂×D₅×SD₁₆	C₂×C₃	1	2	yes	complemented
47	D₅×#127	C₂×C₃	1	1	yes	characteristic
48	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
50	#65452	C₂×C₃	1	2	yes	complemented
51	#65364	C₂×C₃	1	1	yes	characteristic, complemented
52	#65316	C₂×C₃	1	1	yes	characteristic, complemented
53	#65137	C₂×C₃	1	1	yes	characteristic, complemented
54	D₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
55	D₅×#102	C₂×C₃	1	2	yes	complemented
56	#65051	C₂×C₃	1	2	yes	complemented
57	C₂³×C₃×D₅	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
62	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
63	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
64	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
65	C₃×Q₈×D₅	—	2	2	no	—
66	C₃×Q₈×D₅	D₄	1	4	yes	complemented
67	C₃×D₄×D₅	—	2	4	no	—
68	C₃×D₄×D₅	—	2	4	no	—
69	C₃×D₄×D₅	—	4	4	no	—
70	C₃×D₄×D₅	—	4	4	no	—
71	C₂×C₃×D₂₀	—	2	1	no	—
72	C₂×C₃×D₂₀	—	2	1	no	—
73	C₂×C₃×D₂₀	C₂³	1	2	yes	—
74	C₂×C₃×C₄×D₅	—	2	1	no	—
75	C₂×C₃×C₄×D₅	—	2	1	no	—
76	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
77	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
78	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
79	C₂×C₃×Dic₁₀	—	2	1	no	—
80	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
81	C₃×C₅×SD₁₆	—	2	4	no	—
82	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
83	C₃×C₅×C₄⋊C₄	—	2	1	no	—
84	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₃×C₄²×C₅	—	2	1	no	—
86	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
87	C₃×#688	—	2	4	no	—
88	C₃×#687	—	2	4	no	—
89	C₃×C₄⋊Dic₅	—	2	1	no	—
90	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
91	C₃×#683	—	2	1	no	—
92	C₃×#683	—	2	1	no	—
93	C₃×#683	—	2	1	no	—
94	C₃×C₄×Dic₅	—	2	1	no	—
95	C₃×C₄×Dic₅	—	2	1	no	—
96	C₃×C₄×Dic₅	—	2	1	no	—
97	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
98	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
99	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
100	C₂×C₃×#168	C₂³	1	2	yes	—
101	C₃×#677	—	2	4	no	—
102	C₃×C₈×D₅	—	2	4	no	—
103	C₂²×C₃×SD₁₆	—	5	2	no	—
104	C₂×C₃×#127	—	5	1	no	—
105	C₂×C₃×C₄×Q₈	—	5	1	no	—
106	C₃×#460	—	5	2	no	—
107	C₃×#460	—	5	1	no	—
108	C₃×#460	—	5	1	no	—
109	C₃×#460	—	5	1	no	—
110	C₃×#460	—	5	2	no	—
111	C₃×#460	D₅	1	1	yes	characteristic, direct product factor
112	C₂×C₃×C₄⋊C₈	—	5	1	no	—
113	C₂×C₃×#102	—	5	2	no	—
114	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
115	C₂×D₄×D₅	—	2	1	no	—
116	C₂×D₄×D₅	—	2	1	no	—
117	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
118	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
119	C₅×#127	C₂²×C₃	1	1	yes	characteristic
120	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
121	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₂×#688	C₂²×C₃	1	2	yes	complemented
123	#4086	—	2	1	no	—
124	#4086	—	2	1	no	—
125	#4086	C₂²×C₃	1	2	yes	—
126	C₂×#687	C₂²×C₃	1	2	yes	complemented
127	D₅×SD₁₆	—	2	8	no	—
128	C₂×#677	C₂²×C₃	1	2	yes	complemented
129	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
130	D₅×C₄⋊C₄	—	2	1	no	—
131	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	#4033	—	2	1	no	—
133	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
134	#4020	C₂²×C₃	1	1	yes	characteristic
135	C₄²×D₅	—	2	1	no	—
136	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
137	C₄×Dic₁₀	—	2	1	no	—
138	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₅×#102	C₂²×C₃	1	2	yes	complemented
141	#3964	C₂²×C₃	1	2	yes	complemented
142	#3953	C₂²×C₃	1	2	yes	complemented
143	#3946	C₂²×C₃	1	2	yes	complemented
144	#3941	C₂²×C₃	1	2	yes	complemented
145	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₂×#460	—	5	1	no	Sylow
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂²×C₃×D₅	—	2	2	no	—
149	C₂²×C₃×D₅	—	4	4	no	—
150	C₂²×C₃×D₅	—	4	4	no	—
151	C₂²×C₃×D₅	—	4	4	no	—
152	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
153	C₃×C₅×Q₈	—	2	1	no	—
154	C₃×C₅×Q₈	C₂×D₄	1	2	yes	complemented
155	C₃×C₅×D₄	—	2	2	no	—
156	C₃×C₅×D₄	—	2	2	no	—
157	C₃×C₅×D₄	—	4	2	no	—
158	C₃×C₅×D₄	—	4	2	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	1	no	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₃×C₂²⋊D₅	—	4	4	no	—
165	C₃×C₂²⋊D₅	—	4	4	no	—
166	C₃×C₂²⋊D₅	—	4	4	no	—
167	C₂×C₃×Dic₅	—	2	1	no	—
168	C₂×C₃×Dic₅	—	2	1	no	—
169	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
170	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
172	C₃×D₂₀	—	2	2	no	—
173	C₃×D₂₀	—	2	2	no	—
174	C₃×D₂₀	—	4	2	no	—
175	C₃×D₂₀	—	4	2	no	—
176	C₃×C₄×D₅	—	2	4	no	—
177	C₃×C₄×D₅	—	2	2	no	—
178	C₃×C₄×D₅	—	4	2	no	—
179	C₃×C₄×D₅	SD₁₆	1	4	yes	complemented
180	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
181	C₃×C₄×D₅	#41	1	2	yes	—
182	C₃×Dic₁₀	—	2	1	no	—
183	C₃×Dic₁₀	—	2	4	no	—
184	C₃×Dic₁₀	C₂×D₄	1	2	yes	complemented
185	C₃×C₅×C₈	—	2	2	no	—
186	C₃×#168	—	2	2	no	—
187	C₂²×C₃×Q₈	—	5	1	no	—
188	C₂²×C₃×D₄	—	5	2	no	—
189	C₂²×C₃×D₄	—	10	1	no	—
190	C₂²×C₃×D₄	—	10	1	no	—
191	C₂×C₃×SD₁₆	—	5	2	no	—
192	C₂×C₃×SD₁₆	—	5	2	no	—
193	C₂×C₃×SD₁₆	—	5	2	no	—
194	C₂×C₃×SD₁₆	—	10	8	no	—
195	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
196	C₂²×C₃×C₈	—	5	2	no	—
197	C₃×#127	—	5	2	no	—
198	C₃×#127	—	5	1	no	—
199	C₃×#127	—	10	1	no	—
200	C₃×#127	—	10	1	no	—
201	C₃×#127	C₂×D₅	1	1	yes	characteristic
202	C₃×C₄×Q₈	—	5	1	no	—
203	C₃×C₄×Q₈	—	5	1	no	—
204	C₃×C₄×Q₈	—	5	1	no	—
205	C₃×C₄×Q₈	—	10	1	no	—
206	C₃×C₄×Q₈	—	10	1	no	—
207	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
208	C₂×C₃×C₄⋊C₄	—	5	1	no	—
209	C₂×C₃×C₄⋊C₄	—	10	1	no	—
210	C₂×C₃×C₄²	—	5	1	no	—
211	C₂×C₃×C₄²	—	10	1	no	—
212	C₃×C₄⋊C₈	—	5	2	no	—
213	C₃×C₄⋊C₈	—	5	1	no	—
214	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
215	C₃×#102	—	5	2	no	—
216	C₃×#102	—	5	2	no	—
217	C₃×#102	—	5	2	no	—
218	C₃×#102	C₂×D₅	1	2	yes	complemented
219	C₂³×D₅	—	2	2	no	—
220	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₅×D₄	—	2	1	no	—
222	C₂×C₅×D₄	—	2	1	no	—
223	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
224	C₂×C₂²⋊D₅	—	2	2	no	—
225	C₂×C₂²⋊D₅	—	2	2	no	—
226	C₂×C₂²⋊D₅	—	2	2	no	—
227	Q₈×D₅	—	2	2	no	—
228	Q₈×D₅	C₃×D₄	1	4	yes	complemented
229	D₄×D₅	—	2	4	no	—
230	D₄×D₅	—	2	4	no	—
231	D₄×D₅	—	4	4	no	—
232	D₄×D₅	—	4	4	no	—
233	C₂×D₂₀	—	2	1	no	—
234	C₂×D₂₀	—	2	1	no	—
235	C₂×D₂₀	C₂³×C₃	1	2	yes	—
236	C₂×C₄×D₅	—	2	1	no	—
237	C₂×C₄×D₅	—	2	1	no	—
238	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
239	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
240	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
241	C₂×Dic₁₀	—	2	1	no	—
242	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
243	C₅×SD₁₆	—	2	4	no	—
244	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
245	C₅×C₄⋊C₄	—	2	1	no	—
246	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
247	C₄²×C₅	—	2	1	no	—
248	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
249	#688	—	2	4	no	—
250	#687	—	2	4	no	—
251	C₄⋊Dic₅	—	2	1	no	—
252	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
253	#683	—	2	1	no	—
254	#683	—	2	1	no	—
255	#683	—	2	1	no	—
256	C₄×Dic₅	—	2	1	no	—
257	C₄×Dic₅	—	2	1	no	—
258	C₄×Dic₅	—	2	1	no	—
259	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
260	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
261	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
262	C₂×#168	C₂³×C₃	1	2	yes	—
263	#677	—	2	4	no	—
264	C₈×D₅	—	2	4	no	—
265	C₂²×SD₁₆	—	5	2	no	—
266	C₂×#127	—	5	1	no	—
267	C₂×C₄×Q₈	—	5	1	no	—
268	#460	—	5	2	no	—
269	#460	—	5	1	no	—
270	#460	—	5	1	no	—
271	#460	—	5	1	no	—
272	#460	—	5	2	no	—
273	#460	C₃×D₅	1	1	yes	characteristic, direct product factor
274	C₂×C₄⋊C₈	—	5	1	no	—
275	C₂×#102	—	5	2	no	—
276	C₂²×C₃×C₅	—	4	2	no	—
277	C₂²×C₃×C₅	—	4	2	no	—
278	C₂²×C₃×C₅	—	4	2	no	—
279	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₃×D₅	—	4	2	no	—
281	C₂×C₃×D₅	—	4	2	no	—
282	C₂×C₃×D₅	—	4	2	no	—
283	C₂×C₃×D₅	—	8	8	no	—
284	C₂×C₃×D₅	#121	1	2	yes	—
285	C₂×C₃×D₅	C₂×SD₁₆	1	2	yes	—
286	C₂×C₃×D₅	AGL(1,ℤ/8)	1	2	yes	—
287	C₃×C₄×C₅	—	2	2	no	—
288	C₃×C₄×C₅	—	2	1	no	—
289	C₃×C₄×C₅	—	4	1	no	—
290	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	complemented
291	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
292	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
293	C₃×Dic₅	—	2	2	no	—
294	C₃×Dic₅	—	2	1	no	—
295	C₃×Dic₅	—	4	1	no	—
296	C₃×Dic₅	#121	1	2	yes	—
297	C₃×Dic₅	C₂×SD₁₆	1	2	yes	complemented
298	C₂⁴×C₃	—	10	2	no	—
299	C₂×C₃×Q₈	—	5	4	no	—
300	C₂×C₃×Q₈	—	5	1	no	—
301	C₂×C₃×Q₈	—	10	1	no	—
302	C₂×C₃×Q₈	—	10	2	no	—
303	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
304	C₂×C₃×D₄	—	2	1	no	—
305	C₂×C₃×D₄	—	2	1	no	—
306	C₂×C₃×D₄	—	5	2	no	—
307	C₂×C₃×D₄	—	10	4	no	—
308	C₂×C₃×D₄	—	10	4	no	—
309	C₂×C₃×D₄	—	10	2	no	—
310	C₂×C₃×D₄	—	10	2	no	—
311	C₂×C₃×D₄	—	10	2	no	—
312	C₂×C₃×D₄	—	10	1	no	—
313	C₂×C₃×D₄	—	10	1	no	—
314	C₂×C₃×D₄	—	20	4	no	—
315	C₂×C₃×D₄	—	20	4	no	—
316	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
317	C₂²×C₃×C₄	—	5	1	no	—
318	C₂²×C₃×C₄	—	5	1	no	—
319	C₂²×C₃×C₄	—	5	1	no	—
320	C₂²×C₃×C₄	—	10	1	no	—
321	C₂²×C₃×C₄	—	10	1	no	—
322	C₃×SD₁₆	—	2	4	no	—
323	C₃×SD₁₆	—	10	4	no	—
324	C₃×SD₁₆	—	10	4	no	—
325	C₃×SD₁₆	—	10	4	no	—
326	C₂×C₃×C₈	—	5	2	no	—
327	C₂×C₃×C₈	—	10	4	no	—
328	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
329	C₃×C₄⋊C₄	—	2	1	no	—
330	C₃×C₄⋊C₄	—	5	1	no	—
331	C₃×C₄⋊C₄	—	10	1	no	—
332	C₃×C₄⋊C₄	—	10	1	no	—
333	C₃×C₄⋊C₄	—	10	1	no	—
334	C₃×C₄⋊C₄	—	10	1	no	—
335	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
336	C₃×C₄²	—	2	1	no	—
337	C₃×C₄²	—	5	1	no	—
338	C₃×C₄²	—	5	1	no	—
339	C₃×C₄²	—	5	1	no	—
340	C₃×C₄²	—	10	1	no	—
341	C₃×C₄²	—	10	1	no	—
342	C₃×C₄²	—	10	1	no	—
343	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
344	C₂³×C₅	—	2	2	no	—
345	C₂²×D₅	—	2	2	no	—
346	C₂²×D₅	—	4	4	no	—
347	C₂²×D₅	—	4	4	no	—
348	C₂²×D₅	—	4	4	no	—
349	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
350	C₅×Q₈	—	2	1	no	—
351	C₅×Q₈	C₂×C₃×D₄	1	2	yes	complemented
352	C₅×D₄	—	2	2	no	—
353	C₅×D₄	—	2	2	no	—
354	C₅×D₄	—	4	2	no	—
355	C₅×D₄	—	4	2	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
359	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
360	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
361	C₂²⋊D₅	—	4	4	no	—
362	C₂²⋊D₅	—	4	4	no	—
363	C₂²⋊D₅	—	4	4	no	—
364	C₂×Dic₅	—	2	1	no	—
365	C₂×Dic₅	—	2	1	no	—
366	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
367	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
368	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
369	D₂₀	—	2	2	no	—
370	D₂₀	—	2	2	no	—
371	D₂₀	—	4	2	no	—
372	D₂₀	—	4	2	no	—
373	C₄×D₅	—	2	4	no	—
374	C₄×D₅	—	2	2	no	—
375	C₄×D₅	—	4	2	no	—
376	C₄×D₅	C₃×SD₁₆	1	4	yes	complemented
377	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
378	C₄×D₅	C₃×#41	1	2	yes	—
379	Dic₁₀	—	2	1	no	—
380	Dic₁₀	—	2	4	no	—
381	Dic₁₀	C₂×C₃×D₄	1	2	yes	complemented
382	C₅×C₈	—	2	2	no	—
383	#168	—	2	2	no	—
384	C₂²×Q₈	—	5	1	no	—
385	C₂²×D₄	—	5	2	no	—
386	C₂²×D₄	—	10	1	no	—
387	C₂²×D₄	—	10	1	no	—
388	C₂×SD₁₆	—	5	2	no	—
389	C₂×SD₁₆	—	5	2	no	—
390	C₂×SD₁₆	—	5	2	no	—
391	C₂×SD₁₆	—	10	8	no	—
392	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
393	C₂²×C₈	—	5	2	no	—
394	#127	—	5	2	no	—
395	#127	—	5	1	no	—
396	#127	—	10	1	no	—
397	#127	—	10	1	no	—
398	#127	C₂×C₃×D₅	1	1	yes	characteristic
399	C₄×Q₈	—	5	1	no	—
400	C₄×Q₈	—	5	1	no	—
401	C₄×Q₈	—	5	1	no	—
402	C₄×Q₈	—	10	1	no	—
403	C₄×Q₈	—	10	1	no	—
404	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
405	C₂×C₄⋊C₄	—	5	1	no	—
406	C₂×C₄⋊C₄	—	10	1	no	—
407	C₂×C₄²	—	5	1	no	—
408	C₂×C₄²	—	10	1	no	—
409	C₄⋊C₈	—	5	2	no	—
410	C₄⋊C₈	—	5	1	no	—
411	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
412	#102	—	5	2	no	—
413	#102	—	5	2	no	—
414	#102	—	5	2	no	—
415	#102	C₂×C₃×D₅	1	2	yes	complemented
416	C₂×C₃×C₅	—	8	2	no	—
417	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
418	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
419	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₃×D₅	—	8	2	no	—
421	C₃×D₅	#460	1	4	yes	direct product factor
422	C₂³×C₃	—	2	2	no	—
423	C₂³×C₃	—	5	1	no	—
424	C₂³×C₃	—	10	2	no	—
425	C₂³×C₃	—	20	4	no	—
426	C₂³×C₃	—	20	4	no	—
427	C₂³×C₃	—	20	4	no	—
428	C₃×Q₈	—	2	1	no	—
429	C₃×Q₈	—	5	2	no	—
430	C₃×Q₈	—	10	4	no	—
431	C₃×Q₈	—	10	1	no	—
432	C₃×Q₈	D₄×D₅	1	2	yes	complemented
433	C₃×D₄	—	2	2	no	—
434	C₃×D₄	—	2	2	no	—
435	C₃×D₄	—	4	2	no	—
436	C₃×D₄	—	4	2	no	—
437	C₃×D₄	—	10	2	no	—
438	C₃×D₄	—	10	2	no	—
439	C₃×D₄	—	20	2	no	—
440	C₃×D₄	—	20	4	no	—
441	C₃×D₄	—	20	4	no	—
442	C₃×D₄	—	20	4	no	—
443	C₃×D₄	—	20	2	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	5	1	no	—
447	C₂×C₃×C₄	—	5	1	no	—
448	C₂×C₃×C₄	—	5	2	no	—
449	C₂×C₃×C₄	—	5	2	no	—
450	C₂×C₃×C₄	—	5	4	no	—
451	C₂×C₃×C₄	—	5	1	no	—
452	C₂×C₃×C₄	—	10	2	no	—
453	C₂×C₃×C₄	—	10	4	no	—
454	C₂×C₃×C₄	—	10	1	no	—
455	C₂×C₃×C₄	—	10	1	no	—
456	C₂×C₃×C₄	—	20	2	no	—
457	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
458	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
459	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
460	C₃×C₈	—	2	2	no	—
461	C₃×C₈	—	10	2	no	—
462	C₂²×C₅	—	4	2	no	—
463	C₂²×C₅	—	4	2	no	—
464	C₂²×C₅	—	4	2	no	—
465	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
466	C₂×D₅	—	4	2	no	—
467	C₂×D₅	—	4	2	no	—
468	C₂×D₅	—	4	2	no	—
469	C₂×D₅	—	8	8	no	—
470	C₂×D₅	C₃×#121	1	2	yes	—
471	C₂×D₅	C₂×C₃×SD₁₆	1	2	yes	—
472	C₂×D₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
473	C₄×C₅	—	2	1	no	—
474	C₄×C₅	—	2	2	no	—
475	C₄×C₅	—	4	1	no	—
476	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	complemented
477	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
478	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
479	Dic₅	—	2	1	no	—
480	Dic₅	—	2	2	no	—
481	Dic₅	—	4	1	no	—
482	Dic₅	C₃×#121	1	2	yes	—
483	Dic₅	C₂×C₃×SD₁₆	1	2	yes	complemented
484	C₂⁴	—	10	2	no	—
485	C₂×Q₈	—	5	4	no	—
486	C₂×Q₈	—	5	1	no	—
487	C₂×Q₈	—	10	1	no	—
488	C₂×Q₈	—	10	2	no	—
489	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	5	2	no	—
493	C₂×D₄	—	10	4	no	—
494	C₂×D₄	—	10	4	no	—
495	C₂×D₄	—	10	2	no	—
496	C₂×D₄	—	10	2	no	—
497	C₂×D₄	—	10	2	no	—
498	C₂×D₄	—	10	1	no	—
499	C₂×D₄	—	10	1	no	—
500	C₂×D₄	—	20	4	no	—
501	C₂×D₄	—	20	4	no	—
502	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
503	C₂²×C₄	—	5	1	no	—
504	C₂²×C₄	—	5	1	no	—
505	C₂²×C₄	—	5	1	no	—
506	C₂²×C₄	—	10	1	no	—
507	C₂²×C₄	—	10	1	no	—
508	SD₁₆	—	2	4	no	—
509	SD₁₆	—	10	4	no	—
510	SD₁₆	—	10	4	no	—
511	SD₁₆	—	10	4	no	—
512	C₂×C₈	—	5	2	no	—
513	C₂×C₈	—	10	4	no	—
514	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	5	1	no	—
517	C₄⋊C₄	—	10	1	no	—
518	C₄⋊C₄	—	10	1	no	—
519	C₄⋊C₄	—	10	1	no	—
520	C₄⋊C₄	—	10	1	no	—
521	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
522	C₄²	—	2	1	no	—
523	C₄²	—	5	1	no	—
524	C₄²	—	5	1	no	—
525	C₄²	—	5	1	no	—
526	C₄²	—	10	1	no	—
527	C₄²	—	10	1	no	—
528	C₄²	—	10	1	no	—
529	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
530	C₃×C₅	C₂×#460	1	1	yes	characteristic, complemented, Hall
531	C₂²×C₃	—	4	2	no	—
532	C₂²×C₃	—	4	2	no	—
533	C₂²×C₃	—	4	2	no	—
534	C₂²×C₃	—	5	2	no	—
535	C₂²×C₃	—	5	2	no	—
536	C₂²×C₃	—	5	2	no	—
537	C₂²×C₃	—	20	2	no	—
538	C₂²×C₃	—	20	2	no	—
539	C₂²×C₃	—	20	2	no	—
540	C₂²×C₃	—	40	8	no	—
541	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	4	1	no	—
545	C₃×C₄	—	5	2	no	—
546	C₃×C₄	—	5	2	no	—
547	C₃×C₄	—	10	1	no	—
548	C₃×C₄	—	10	2	no	—
549	C₃×C₄	—	20	1	no	—
550	C₃×C₄	D₅×SD₁₆	1	2	yes	complemented
551	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
552	C₃×C₄	D₅×#41	1	1	yes	characteristic
553	C₂×C₅	—	8	2	no	—
554	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
555	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
556	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
557	D₅	—	8	2	no	—
558	D₅	C₃×#460	1	4	yes	direct product factor
559	C₂³	—	2	2	no	—
560	C₂³	—	5	1	no	—
561	C₂³	—	10	2	no	—
562	C₂³	—	20	4	no	—
563	C₂³	—	20	4	no	—
564	C₂³	—	20	4	no	—
565	Q₈	—	2	1	no	—
566	Q₈	—	5	2	no	—
567	Q₈	—	10	4	no	—
568	Q₈	—	10	1	no	—
569	Q₈	C₃×D₄×D₅	1	2	yes	complemented
570	D₄	—	2	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	10	2	no	—
575	D₄	—	10	2	no	—
576	D₄	—	20	2	no	—
577	D₄	—	20	4	no	—
578	D₄	—	20	4	no	—
579	D₄	—	20	4	no	—
580	D₄	—	20	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	5	1	no	—
584	C₂×C₄	—	5	1	no	—
585	C₂×C₄	—	5	2	no	—
586	C₂×C₄	—	5	2	no	—
587	C₂×C₄	—	5	4	no	—
588	C₂×C₄	—	5	1	no	—
589	C₂×C₄	—	10	2	no	—
590	C₂×C₄	—	10	4	no	—
591	C₂×C₄	—	10	1	no	—
592	C₂×C₄	—	10	1	no	—
593	C₂×C₄	—	20	2	no	—
594	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
595	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
596	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
597	C₈	—	2	2	no	—
598	C₈	—	10	2	no	—
599	C₂×C₃	—	5	4	no	—
600	C₂×C₃	—	8	2	no	—
601	C₂×C₃	—	40	2	no	—
602	C₂×C₃	D₅×#121	1	1	yes	characteristic
603	C₂×C₃	C₂×D₅×SD₁₆	1	1	yes	characteristic
604	C₂×C₃	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic
605	C₅	C₂×C₃×#460	1	1	yes	characteristic, complemented, Sylow
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	5	2	no	—
610	C₂²	—	5	2	no	—
611	C₂²	—	5	2	no	—
612	C₂²	—	20	2	no	—
613	C₂²	—	20	2	no	—
614	C₂²	—	20	2	no	—
615	C₂²	—	40	8	no	—
616	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	5	2	no	—
621	C₄	—	5	2	no	—
622	C₄	—	10	1	no	—
623	C₄	—	10	2	no	—
624	C₄	—	20	1	no	—
625	C₄	C₃×D₅×SD₁₆	1	2	yes	complemented
626	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
627	C₄	C₃×D₅×#41	1	1	yes	characteristic
628	C₃	D₅×#460	1	1	yes	characteristic, direct product factor, Sylow
629	C₂	—	5	4	no	—
630	C₂	—	8	2	no	—
631	C₂	—	40	2	no	—
632	C₂	C₃×D₅×#121	1	1	yes	characteristic
633	C₂	C₂×C₃×D₅×SD₁₆	1	1	yes	characteristic
634	C₂	C₃×D₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#460	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×D₅×#127	C₂
hypercenter	C₃×#460	D₅
hypocenter	C₅	C₂×C₃×#460
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#460

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×D₅×SD₁₆	C₂	semidirect
3. C₃×C₄×Q₈×D₅	C₂	semidirect
4. C₃×C₅×#460	C₂	semidirect
5. C₃×#65452	C₂	semidirect
6. C₃×#65364	C₂	semidirect
7. C₃×#65316	C₂	semidirect
8. C₃×#65137	C₂	semidirect
9. C₃×D₅×C₄⋊C₈	C₂	semidirect
10. C₃×D₅×#102	C₂	semidirect
11. C₃×#65051	C₂	semidirect
12. D₅×#460	C₃	direct (N × H)
17. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₃×C₄×C₅×Q₈	C₂²	semidirect
20. C₃×Q₈×Dic₅	C₂²	semidirect
21. C₂×C₃×#688	C₂²	semidirect
25. C₂×C₃×#687	C₂²	semidirect
27. C₂×C₃×#677	C₂²	semidirect
32. C₃×#4033	C₂²	semidirect
37. C₃×C₄×Dic₁₀	C₂²	semidirect
38. C₃×C₅×C₄⋊C₈	C₂²	semidirect
39. C₃×C₅×#102	C₂²	semidirect
40. C₃×#3964	C₂²	semidirect
41. C₃×#3953	C₂²	semidirect
42. C₃×#3946	C₂²	semidirect
43. C₃×#3941	C₂²	semidirect
44. C₃×C₄⋊#168	C₂²	semidirect
46. C₂×D₅×SD₁₆	C₂×C₃	semidirect
48. C₄×Q₈×D₅	C₂×C₃	semidirect
49. C₅×#460	C₂×C₃	semidirect
50. #65452	C₂×C₃	semidirect
51. #65364	C₂×C₃	semidirect
52. #65316	C₂×C₃	semidirect
53. #65137	C₂×C₃	semidirect
54. D₅×C₄⋊C₈	C₂×C₃	semidirect
55. D₅×#102	C₂×C₃	semidirect
56. #65051	C₂×C₃	semidirect
66. C₃×Q₈×D₅	D₄	semidirect
111. C₃×#460	D₅	direct (N × H)
118. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
120. C₄×C₅×Q₈	C₂²×C₃	semidirect
121. Q₈×Dic₅	C₂²×C₃	semidirect
122. C₂×#688	C₂²×C₃	semidirect
126. C₂×#687	C₂²×C₃	semidirect
128. C₂×#677	C₂²×C₃	semidirect
133. #4033	C₂²×C₃	semidirect
138. C₄×Dic₁₀	C₂²×C₃	semidirect
139. C₅×C₄⋊C₈	C₂²×C₃	semidirect
140. C₅×#102	C₂²×C₃	semidirect
141. #3964	C₂²×C₃	semidirect
142. #3953	C₂²×C₃	semidirect
143. #3946	C₂²×C₃	semidirect
144. #3941	C₂²×C₃	semidirect
145. C₄⋊#168	C₂²×C₃	semidirect
154. C₃×C₅×Q₈	C₂×D₄	semidirect
179. C₃×C₄×D₅	SD₁₆	semidirect
184. C₃×Dic₁₀	C₂×D₄	semidirect
195. C₂×C₃×SD₁₆	C₂×D₅	semidirect
207. C₃×C₄×Q₈	C₂×D₅	semidirect
214. C₃×C₄⋊C₈	C₂×D₅	semidirect
218. C₃×#102	C₂×D₅	semidirect
228. Q₈×D₅	C₃×D₄	semidirect
273. #460	C₃×D₅	direct (N × H)
290. C₃×C₄×C₅	C₂×SD₁₆	semidirect
297. C₃×Dic₅	C₂×SD₁₆	semidirect
351. C₅×Q₈	C₂×C₃×D₄	semidirect
376. C₄×D₅	C₃×SD₁₆	semidirect
381. Dic₁₀	C₂×C₃×D₄	semidirect
392. C₂×SD₁₆	C₂×C₃×D₅	semidirect
404. C₄×Q₈	C₂×C₃×D₅	semidirect
411. C₄⋊C₈	C₂×C₃×D₅	semidirect
415. #102	C₂×C₃×D₅	semidirect
421. C₃×D₅	#460	direct (N × H)
432. C₃×Q₈	D₄×D₅	semidirect
476. C₄×C₅	C₂×C₃×SD₁₆	semidirect
483. Dic₅	C₂×C₃×SD₁₆	semidirect
530. C₃×C₅	C₂×#460	semidirect
550. C₃×C₄	D₅×SD₁₆	semidirect
558. D₅	C₃×#460	direct (N × H)
569. Q₈	C₃×D₄×D₅	semidirect
605. C₅	C₂×C₃×#460	semidirect
625. C₄	C₃×D₅×SD₁₆	semidirect
628. C₃	D₅×#460	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×D₅×SD₁₆	2
C₃×D₅×#127	2
C₃×C₄×Q₈×D₅	2
C₃×C₅×#460	2
C₃×#65452	2
C₃×#65364	2
C₃×#65316	2
C₃×#65137	2
C₃×D₅×C₄⋊C₈	2
C₃×D₅×#102	2
C₃×#65051	2
D₅×#460	3
C₂×C₃×#460	5

Subgroups — C3×D5×#460 #14426005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#460 #14426005